## Appendix A: complete expressions of the ions and neutrals velocitiesIn Hénoux and Somov (1991), velocities of electrons, ions and neutrals have been computed, for an axially symmetrical magnetic field, in the three fluids approximation, by solving the equations that express the balance of the horizontal forces acting per unit volume on each particle fluid, i.e. Here is the friction force due to particles
The horizontal velocities of ions and neutrals derived from the equations above are (Hénoux and Somov, 1991): The ions and neutrals velocities in these equations are relatives to the velocities in the convective zone, since all components of the vector have been replaced by . The function is given by: where is the electric conductivity parallel to . where and are the collision frequencies between electrons, ions and neutrals and between electrons and ions. and are the contributions to and of the inertial terms. They are given by: The summation is made over all species, electrons, ions and neutrals. The azimuthal and radial current densities are found to be where is the vertical current density. is defined by where is defined by : The subscripts refer to the azimuthal,
radial and vertical components of the magnetic and velocity fields.
The subscripts The equation (A.11) can be rewritten as ## Appendix B: radial velocities of ions and neutralsAssuming no radial motions in the convective zone and that the radial component of is null, we can write the radial velocities of neutrals and ions as : Neglecting the contribution of electrons and in the hypothesis that , we obtain from equations (A.7) and (A.12) . Consequently the radial velocities of ions and neutrals are given by ## Appendix C: azimuthal velocity of neutralsThe radial dependence of can be derived
from equations (A.5) and (A.10). Considering successively the various
terms on the RHS of eq.(A.5) we show below that the last term is the
dominant term on the RHS of this equation. © European Southern Observatory (ESO) 1997 Online publication: July 3, 1998 |